It is known that x1 and x2 are roots of the equation x2−8x+k=0, where 3x1+4x2=29. find k.

Answer:k = 15Step-by-step explanation:∵ x² - 8x + k = 0 ⇒ has two roots x1 and x2∵ ax² + bx + c = 0 has two roots∴ The sum of roots = -b/a and the product of them = c/a∵ a = 1 , b = -8 and c = k∴ x1 + x2 = -(-8)/1 = 8∴ x1 + x2 = 8 ⇒ (1)∵ 3x1 + 4x2 = 29 ⇒ (2) Multiply (1) by -4∴ -4x1 - 4x2 = -32 ⇒ (3) Add (2) and (3)∴ -x1 = -3∴ x1 = 3By substituting value of x1 in (1)∴ 3 + x2 = 8∴ x2 = 5∴ The roots are 3 and 5∴ c/a = 3 × 5 = 15 ⇒ (a = 1)∴ c = 15∴ k = 15